Question

find the range of following function:

f(x)=3/(2-x2)

Answer 1

$y = \frac{3}{ 2 - {x}^{2} }$
$y(2 - {x}^{2} ) = 3$
$2y - y {x}^{2} = 3 \\ - y {x}^{2} = 3 - 2y$
${x}^{2} = \frac{3 - 2y}{ - y}$
or
${x}^{2} = \frac{2y - 3}{y}$
$x = \sqrt{ \frac{2y - 3}{y} }$
now the value of y for which function is defined is called range.
so for y=0 ,function goes infinite.
the values of y for which the square root does not include negative values, for values of y from. - infinite to 1 the value of square root is -ve.
so range exclude all the values for which function does not contain real values
so range is R-[- infinite to 1]